# `y = e^x` Use the derivative to determine whether the function is strictly monotonic on its entire domain and therefore has an inverse function.

*print*Print*list*Cite

Expert Answers

embizze | Certified Educator

We are asked to determine if the function ` y=e^x ` has an inverse function by finding if the function is strictly monotonic on its entire domain using the derivative. The domain is all reals.

`y'=e^x ` and ` e^x>0` for all real x so the function is strictly monotonic (in this case strictly increasing) on its entire domain and thus has an inverse function.

The graph: